Problem: Solve for $x$ and $y$ using substitution. ${-6x-6y = 12}$ ${x = -4y+1}$
Explanation: Since $x$ has already been solved for, substitute $-4y+1$ for $x$ in the first equation. ${-6}{(-4y+1)}{- 6y = 12}$ Simplify and solve for $y$ $24y-6 - 6y = 12$ $18y-6 = 12$ $18y-6{+6} = 12{+6}$ $18y = 18$ $\dfrac{18y}{{18}} = \dfrac{18}{{18}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x = -4y+1}\thinspace$ to find $x$ ${x = -4}{(1)}{ + 1}$ $x = -4 + 1$ ${x = -3}$ You can also plug ${y = 1}$ into $\thinspace {-6x-6y = 12}\thinspace$ and get the same answer for $x$ : ${-6x - 6}{(1)}{= 12}$ ${x = -3}$